Theoretical and numerical structure for reacting shock waves
SIAM Journal on Scientific and Statistical Computing
A study of numerical methods for hyperbolic conservation laws with stiff source terms
Journal of Computational Physics
Numerical study of the mechanisms for initiation for reacting shock waves
SIAM Journal on Scientific and Statistical Computing
Theoretical and numerical structure for unstable one-dimensional detonations
SIAM Journal on Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Multiresolution schemes for the reactive Euler equations
Journal of Computational Physics
The random projection method for hyperbolic conservation laws with stiff reaction terms
Journal of Computational Physics
The random projection method for stiff multispecies detonation capturing
Journal of Computational Physics
A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves
SIAM Journal on Scientific Computing
The Random Projection Method for Stiff Detonation Capturing
SIAM Journal on Scientific Computing
Numerical solution of under-resolved detonations
Journal of Computational Physics
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
Journal of Computational Physics
ADER Schemes for Nonlinear Systems of Stiff Advection---Diffusion---Reaction Equations
Journal of Scientific Computing
Journal of Computational Physics
Propagation of ocean surface waves on a spherical multiple-cell grid
Journal of Computational Physics
Hi-index | 31.45 |
A new fractional-step method is proposed for numerical simulations of hyperbolic conservation laws with stiff source terms arising from chemically reactive flows. In stiff reaction problems, a well-known spurious numerical phenomenon, the incorrect propagation speed of discontinuities, may occur in general fractional-step algorithm due to the underresolved numerical solution in both space and time. The basic idea of the present proposed scheme is to replace the cell average representation with a two-equilibrium states reconstruction during the reaction step, which allows us to obtain the correct propagation of discontinuities for stiff reaction problems in an underresolved mesh. Because the definition of these two-equilibrium states for each transition cell is independent of its neighboring cells, the proposed method can be extended to multi-dimensional problems directly. In addition, this method is promising to deal with more complicated real-world problems after being extended to multi-species/multi-reactions system. Extensive numerical examples for one- and two-dimensional scalar and Euler system demonstrate the reliability and robustness of this novel method.